{
  "id": "1712.05434",
  "version": "v1",
  "published": "2017-12-14T20:01:53.000Z",
  "updated": "2017-12-14T20:01:53.000Z",
  "title": "On the cohomological spectrum and support varieties for infinitesimal unipotent supergroup schemes",
  "authors": [
    "Christopher M. Drupieski",
    "Jonathan R. Kujawa"
  ],
  "comment": "35 pages",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We show that if $G$ is an infinitesimal elementary supergroup scheme of height $\\leq r$, then the cohomological spectrum $|G|$ of $G$ is naturally homeomorphic to the variety $\\mathcal{N}_r(G)$ of supergroup homomorphisms $\\rho: \\mathbb{M}_r \\rightarrow G$ from a certain (non-algebraic) affine supergroup scheme $\\mathbb{M}_r$ into $G$. In the case $r=1$, we further identify the cohomological support variety of a finite-dimensional $G$-supermodule $M$ as a subset of $\\mathcal{N}_1(G)$. We then discuss how our methods, when combined with recently-announced results by Benson, Iyengar, Krause, and Pevtsova, can be applied to extend the homeomorphism $\\mathcal{N}_r(G) \\cong |G|$ to arbitrary infinitesimal unipotent supergroup schemes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-14T20:01:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G10",
      "17B56"
    ],
    "keywords": [
      "support variety",
      "cohomological spectrum",
      "arbitrary infinitesimal unipotent supergroup schemes",
      "infinitesimal elementary supergroup scheme",
      "affine supergroup scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}